The contributions of the heavy scalar to the oblique parameters
\(\Delta \mathcal {O}_{i} \equiv \mathcal {O}_{i}-\mathcal {O}_{i}^{\rm SM}\) 
(here \(i\)  denotes \(T\) , \(S\) , or \(U\) ) can be quantified as follows [1]}, [2]}:
\(\Delta T&= \frac{3}{16 \pi s_{W}^{2}}\left[\cos ^{2} \theta \left\lbrace f_{T}\left(\frac{m_{\mathcal {H}}^{2}}{m_{W}^{2}}\right)-\frac{1}{c_{W}^{2}} f_{T}\left(\frac{m_{\mathcal {H}}^{2}}{m_{Z}^{2}}\right)\right\rbrace +\sin ^{2} \theta \left\lbrace f_{T}\left(\frac{m_{\mathcal {S}}^{2}}{m_{W}^{2}}\right)\right.\right.\\& \qquad \qquad \left.\left.-\frac{1}{c_{W}^{2}} f_{T}\left(\frac{m_{\mathcal {S}}^{2}}{m_{Z}^{2}}\right)\right\rbrace -\left\lbrace f_{T}\left(\frac{m_{\mathcal {H}}^{2}}{m_{W}^{2}}\right)-\frac{1}{c_{W}^{2}} f_{T}\left(\frac{m_{\mathcal {H}}^{2}}{m_{Z}^{2}}\right)\right\rbrace \right],\\\Delta S&= \frac{1}{2 \pi }\left[\cos ^{2} \theta f_{S}\left(\frac{m_{\mathcal {H}}^{2}}{m_{Z}^{2}}\right)+\sin ^{2}\theta f_{S}\left(\frac{m_{\mathcal {S}}^{2}}{m_{Z}^{2}}\right)-f_{S}\left(\frac{m_{\mathcal {H}}^{2}}{m_{Z}^{2}}\right)\right],\\\Delta U&= \frac{1}{2 \pi }\left[\cos ^{2} \theta f_{S}\left(\frac{m_{\mathcal {H}}^{2}}{m_{W}^{2}}\right)+\sin ^{2} \theta f_{S}\left(\frac{m_{\mathcal {S}}^{2}}{m_{W}^{2}}\right)-f_{S}\left(\frac{m_{\mathcal {H}}^{2}}{m_{W}^{2}}\right)\right]-\Delta S,\) 
